Vol. 9, No. 5, 2014

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Transient elastic-viscoplastic dynamics of thin sheets

Ali A. Atai and David J. Steigmann

Vol. 9 (2014), No. 5, 557–574

A model for the finite transient viscoplastic response of thin membranes is derived from three-dimensional viscoplasticity theory for isotropic materials. This accommodates large elastic strains and is not limited to conventional Kirchhoff–Love kinematics. In particular, we show that the Kirchhoff–Love hypothesis need not obtain in the presence of plastic deformation. Numerical experiments exhibit large transient elastic strains accompanied by small deviations from Kirchhoff–Love kinematics.

Dedicated to José J. A. Rodal

viscoplasticity, membranes, transient response
Received: 31 July 2014
Revised: 18 September 2014
Accepted: 26 September 2014
Published: 14 December 2014
Ali A. Atai
School of Mechanical Engineering
College of Engineering
University of Tehran
PO Box 4563-11155
Tehran 11155
David J. Steigmann
Department of Mechanical Engineering
University of California
6133 Etcheverry Hall
Berkeley, CA 94720-1740
United States